CN104063838B - Asymmetric Watermarking Schemes method based on Logistic chaotic maps and Walsh sequences - Google Patents

Abstract

The present invention provides a kind of asymmetrical watermarking algorithm based on Logistic chaotic map and Walsh sequence, comprises the following steps: obtain feature matrix according to the maximum singular value of each coefficient block of carrier image; Select the Walsh sequence unrelated to feature matrix as common key watermark, get the chaotic sequence according to the Logistic mapping dynamic equation, convert the chaotic sequence into a sequence with a value of ±1 and intercept a sequence unrelated to the feature matrix as the private key watermark; according to the public key watermark and the private key The weighted sum of the watermarks is used to obtain the embedded watermark, and the watermarked image is generated according to the information embedded in the watermark; the watermarked image is detected. The technical scheme of the invention has high safety, can better protect copyright, has good detection performance and strong robustness.

Description

Asymmetric Watermarking Method Based on Logistic Chaos Map and Walsh Sequence

technical field

The invention belongs to the technical field of digital watermarking, and in particular relates to an asymmetrical watermarking method based on Logistic chaotic mapping and Walsh sequences.

Background technique

With the widespread popularization of digital products and the rapid development of network technology, people pay more and more attention to the security of digital products. How to effectively protect the copyright of products has become an issue of great concern to people.

Digital watermarking technology can protect the copyright of digital products very well. However, digital watermarking technology generally uses symmetric watermarking. For traditional symmetric digital watermarking technology, the same key is used for watermark embedding and watermark detection. Watermark detection can only be completed by copyright owners and authorized institutions. The owner needs to show the private key to prove its legal possession. And once the key is exposed, the attacker can remove or forge the watermark, so the copyright cannot be well protected.

Contents of the invention

The purpose of the present invention is to provide an asymmetric watermarking method based on Logistic chaotic map and Walsh sequence to solve the above problems.

In order to achieve the above object, the technical solution adopted in the present invention is:

A kind of asymmetrical watermark method based on Logistic chaotic map and Walsh sequence, it is characterized in that, comprises the steps:

Step 1: Construction of the feature matrix S

Take the m×m image A _m×m as the carrier image, perform DCT transformation on the carrier image, select 4k×4k intermediate frequency coefficients from the DCT coefficients, and form a matrix B _4k×4k ,

Divide the matrix B _4k×4k into N blocks of non-overlapping 4×4 coefficient blocks, N=k×k,

Denote the i-th coefficient block as B _i , i∈[1,N], according to [u _i , s _i , v _i ]=svd(B _i ), perform singular value decomposition on each coefficient block and extract each block The largest singular value of , a total of N largest singular values are obtained, and the N largest singular values form a characteristic matrix S;

Step 2: Construction of public key watermark W _p and private key watermark W _s

Select a Walsh sequence of length N that is not related to the feature matrix S as the public key watermark W _p , namely

According to the Logistic mapping dynamic equation x _n+1 = μ ₀ x _n (1-x _n ), the chaotic sequence X={x ₁ ,x ₂ ,Λ,x _n } is obtained, where μ ₀ is the branch parameter, μ ₀ ∈ (0,4), the initial value of x x ₀ ∈ (0,1),

According to x _i =mod(round(x _i ×10 ⁸ ),2), Convert the chaotic sequence X into a sequence with a value of ±1, mod means modulo operation, round means rounding to the nearest integer,

From the sequence with a value of ±1, intercept a sequence Y={y ₁ ,y ₂ ,Λ,y _N } with a length of N that is not related to the feature matrix S as the private key watermark W _s , namely

The construction of the above public key watermark W _p and private key watermark W _s has no sequence;

Step 3: Generate watermark image A' _m×m

Calculate the weighted sum of the public key watermark W _p and the private key watermark W _s , and get the embedded watermark W _w according to the weighted sum construction,

According to S'=S+λW _w , the information embedded in the watermark W _w is embedded in the feature matrix S by addition to obtain the feature matrix S', and the singular value corresponding to each coefficient block in the feature matrix S' is subjected to singular value inverse transformation, Obtain the modified DCT coefficients, and use the modified DCT coefficients to perform DCT inverse transformation on the carrier image to obtain an m×m watermark image A′ _m×m ;

Step 4: Watermark detection

For the watermark image A' _m×m , adopt the operation of step 1 to obtain the characteristic matrix S', the characteristic matrix S'=S+λW _w +n ₀ =S+λ(αW _s +βW _p )+n ₀ , n ₀ means Interference signals caused by various attacks,

Use W _p _threshold and W _s _threshold to represent the public key detection threshold and private key detection threshold respectively,

The method of setting the public key detection threshold W _p _threshold is: in, is the mean value of the characteristic matrix S, is the mean value of the public key watermark W _p , is the energy of the public key watermark W _p ,

According to the setting method of the public key detection threshold W _p _threshold, set the private key detection threshold W _s _threshold,

Use W _p _test and W _s _test to represent the detection value of the public key detection and the detection value of the private key detection respectively, according to the formula:

Calculate W _p _test, refer to the same calculation method to calculate W _s _test,

Comparing W _{p _test with W p _threshold} , when W _p _test ≥ W _p _threshold, it is determined that the public key watermark W _p exists, otherwise, it is determined that the public key watermark W _p does not exist,

Comparing W _{s _test with W s _threshold} , when W _s _test≥W _s _threshold, it is determined that the private key watermark W _s exists, otherwise, it is determined that the private key watermark W _s does not exist.

The further feature of the technical solution of the present invention is that in step 1, the DCT coefficients are zigzag scanned, and the DCT coefficients are sorted by frequency from low to high.

A further feature of the technical solution of the present invention is that the image A _m×m is a grayscale image.

The further feature of the technical solution of the present invention is that in step 2, the value range of the branch parameter μ ₀ is 3.5699456≤μ ₀ ≤4.

The technical solution of the present invention is further characterized in that: the construction method of the embedded watermark W _w in Step 3 is: W _w =αW _s +βW _p , where α,β∈(0,1).

Compared with the background technology, the advantages and positive effects of the technical solution of the present invention are as follows:

1. High security, better copyright protection

According to the technical solution provided by the present invention, the weighted sum of the public key watermark W _p and the private key watermark W _s is used to construct the embedded watermark. Compared with the background technology, when a copyright dispute occurs, the copyright owner does not need to expose the private key watermark , the public key watermark can be directly used for detection. Even if the watermark attacker masters the private key watermark, he cannot deduce the embedded key.

2. Good detection performance and strong robustness

The technical scheme of the present invention adopts the asymmetric watermarking method based on the Logistic chaotic map and the Walsh sequence to embed the watermark in the carrier image, has good detection performance, and has good robustness against attacks such as additive noise, lossy compression, and cropping.

Description of drawings

Fig. 1 is the carrier image of the technical solution of the present invention in an embodiment;

Fig. 2 is a watermark embedding flow chart of the technical solution of the present invention in an embodiment;

Fig. 3 is the flow chart of watermark detection in the embodiment of the technical solution of the present invention;

Fig. 4 is the watermark image of the technical solution of the present invention in the embodiment;

Fig. 5 is the watermark detection result under JPEG compression of the technical solution of the present invention in the embodiment; And

Fig. 6 is an explanatory diagram of the detection results of different detection sequences when Gaussian noise is added in the embodiment of the technical solution of the present invention.

detailed description

The asymmetric watermarking method based on the Logistic chaotic map and the Walsh sequence involved in the present invention will be further described below in conjunction with the accompanying drawings.

<Example>

Fig. 1 is a carrier image of the technical solution of the present invention in an embodiment.

In this embodiment, under the environment of matlab 2013a, a 512×512 grayscale image as shown in FIG. 1 is used as a carrier image (ie, m=512). Take the branch parameter μ ₀ =3.711 of the one-dimensional Logistic chaotic sequence, and the initial value x ₀ =0.773. The public key W _p is selected as the Walsh sequence formed by the 112th row of the 4096×4096 Hadamard matrix. When embedding watermark W _w , parameters α=0.73, β=0.64, λ=17.

Fig. 2 is a flow chart of watermark embedding in an embodiment of the technical solution of the present invention.

Fig. 3 is a flow chart of watermark detection in an embodiment of the technical solution of the present invention.

In the asymmetric watermarking method based on the Logistic chaotic map and the Walsh sequence provided in this embodiment, the Logistic chaotic map and the Walsh sequence are first used to construct the embedded watermark, and then the watermark is embedded into the feature matrix composed of the largest singular value of the carrier image, and the The correlation value calculation method detects the watermark. Specifically include the following steps as shown in Figure 2 and Figure 3:

Step 1: Construction of the feature matrix S

Take the m×m image A _m×m shown in Figure 1 as the carrier image, m=512, carry out DCT transformation on the carrier image, and perform zigzag scanning on the DCT coefficients, and select 4k× from the DCT coefficients 4k intermediate frequency coefficients form a matrix B _4k×4k ,

Divide the matrix B _4k×4k into N non-overlapping 4×4 coefficient blocks, N=k×k, denote the i-th coefficient block as B _i , i∈[1,N], according to [u _i , s _i ,v _i ]=svd(B _i ), perform singular value decomposition on each block of coefficients and extract the maximum singular value of each block, that is, s _i (1,1), to obtain N maximum singular values in total, and take N The largest singular values constitute the characteristic matrix S.

Step 2: Construction of public key watermark W _p and private key watermark W _s

Select a Walsh sequence of length N that is not related to the feature matrix S as the public key watermark W _p , namely

Take the branch parameter μ ₀ = 3.711, the initial value x ₀ = 0.773, and substitute it into the Logistic mapping dynamic equation x _n+1 = μ ₀ x _n (1-x _n ), to obtain the chaotic sequence X={x ₁ ,x ₂ , Λ,x _n }.

According to x _i =mod(round(x _i ×10 ⁸ ),2), Convert the chaotic sequence X to a sequence with a value of ±1, mod means modulo operation, and round means round to the nearest integer.

From the sequence with a value of ±1, intercept a sequence Y={y ₁ ,y ₂ ,Λ,y _N } with a length of N that is not related to the feature matrix S as the private key watermark W _s , namely

Fig. 4 is a watermark image in an embodiment of the technical solution of the present invention.

Step 3: Generate watermark image A' _m×m

Set parameters α=0.73, β=0.64, λ=17.

The weighted sum of the public key watermark W _p and the private key watermark W _s is used to construct the embedded watermark W _w , W _w =αW _s +βW _p .

According to S'=S+λW _w , the information embedded in the watermark W _w is embedded in the feature matrix S by addition to obtain the feature matrix S', and the singular value corresponding to each coefficient block in the feature matrix S' is subjected to singular value inverse transformation, The modified DCT coefficients are obtained, and the carrier image is subjected to inverse DCT transformation using the modified DCT coefficients to obtain an m×m watermark image A' _m×m as shown in Figure 4 .

Step 4: Watermark detection

For the watermark image A' _m×m , adopt the operation of step 1 to obtain the characteristic matrix S', the characteristic matrix S'=S+λW _w +n ₀ =S+λ(αW _s +βW _p )+n ₀ , n ₀ means Interference signals caused by various attacks,

Use W _p _threshold and W _s _threshold to represent the public key detection threshold and private key detection threshold respectively,

The method of setting the public key detection threshold W _p _threshold is: in, is the mean value of the characteristic matrix S, is the mean value of the public key watermark W _p , is the energy of the public key watermark W _p ,

According to the setting method of the public key detection threshold W _p _threshold, set the private key detection threshold W _s _threshold,

Use W _p _test and W _s _test to represent the detection value of the public key detection and the detection value of the private key detection respectively, according to the formula:

Since the constructed W _p , W _s and the characteristic matrix S satisfy the following relationship:

but: The public key detection threshold W _p _threshold is set as: in is the mean value of all elements in the feature matrix S, is the mean value of the public key, is the energy of the public key. Similarly, the private key detection threshold W _s _threshold can be obtained.

Compare W _{p _test with W p _threshold} , when W _p _test ≥ W _p _threshold, it is determined that the public key watermark W _p exists, otherwise, it is determined that the public key watermark W _p does not exist; compare W _{s _test with W s _threshold} In comparison, when W _s _test≥W _s _threshold, it is determined that the private key watermark W _s exists, otherwise, it is determined that the private key watermark W _s does not exist.

The watermarked image A' _m×m shown in Figure 4 is subjected to JPEG compression, Gaussian noise, salt and pepper noise, and shearing attacks.

Fig. 5 is the watermark detection result under JPEG compression in the embodiment of the technical solution of the present invention.

JPEG compression: The watermark image A' _m×m shown in Figure 4 is subjected to different degrees of JPEG compression processing, and then the watermark detection is performed, and the detection effect is shown in Figure 5. It can be seen from Figure 5 that the public key detection and private key detection are still effective and the detection performance is good when the watermark image is compressed by JPEG with a quality factor of 20%.

Add Gaussian noise:

(1) Gaussian noise is added to the watermark image A' _m×m shown in Figure 4. The variance of the noise is 0.006, 0.009, and 0.012 respectively. The watermark detection results are shown in Table 1. It can be seen from Table 1 that the method provided by this embodiment has better ability to resist Gaussian noise interference.

Table 1 Watermark detection results after adding Gaussian noise

Fig. 6 is an explanatory diagram of the detection results of different detection sequences when Gaussian noise is added in the embodiment of the technical solution of the present invention.

(2) Gaussian noise is added to the watermark image A' _m×m shown in Figure 4, the noise variance is: 0.009, and 1000 sequences are used for detection, of which the 200th detection sequence is the private key watermark, and the 400th detection sequence is the public key watermark. key watermark, and other detection sequences are 998 Walsh sequences formed from the 200th row to the 1197th row of the 4096×4096 Hadamard matrix. The results of watermark detection are shown in Figure 6.

Add salt and pepper noise: Add salt and pepper noise to the watermark image A' _m×m shown in Figure 4, the noise intensity is 0.01, 0.03, 0.04 respectively, and the watermark detection results are shown in Table 2. It can be seen from Table 2 that the method of the present invention has a better ability to resist salt and pepper noise interference.

Table 2 Watermark detection results after adding different intensities of salt and pepper noise

Cutting: The watermark image A' _m×m shown in Figure 4 is cut to different degrees, and the watermark detection results are shown in Table 3. As can be seen from Table 3, the method of the present invention has better shear resistance.

Table 3 Detection results of different degrees of cut watermarks

Compared with the background technology, the advantages and positive effects of the technical solution provided by this embodiment are as follows:

1. High security, better copyright protection

According to the technical solution provided by this embodiment, the weighted sum of the public key watermark W _p and the private key watermark W _s is used to construct the embedded watermark. Compared with the background technology, when a copyright dispute occurs, the copyright owner does not need to disclose the private key The watermark can be detected directly by using the public key watermark. Even if the watermark attacker has mastered the private key watermark, he cannot deduce the embedded key.

2. Good detection performance and strong robustness

The technical solution provided in this embodiment adopts the asymmetric watermark method based on Logistic chaotic map and Walsh sequence to embed watermark in the carrier image, and the attack tests such as JPEG compression, adding Gaussian noise, adding salt and pepper noise, and shearing show that the method described in this embodiment The provided technical solution has good detection performance and is robust to attacks such as additive noise, lossy compression, and cropping.

Of course, the asymmetric watermarking method based on the Logistic chaotic map and the Walsh sequence involved in the present invention is not limited to the content in the above-mentioned embodiments. The above content is only a basic description of the concept of the present invention, and any equivalent transformation made according to the technical solution of the present invention belongs to the protection scope of the present invention.

In addition, in the above-mentioned embodiment, a grayscale image of 512×512 is selected as the carrier image. In the technical solution of the present invention, a square image of any length can be selected as the carrier image. The square image can be a grayscale image, or For color images, the same effect can be achieved.

In addition, in the above example, the branch parameter μ ₀ =3.711, the initial value x ₀ =0.773, the branch parameter μ ₀ of the technical solution of the present invention can be selected from any value between 0-4, and x ₀ can be selected from 0 to Any value between 1 can achieve the same effect.

In addition, in the above embodiment, the parameters α=0.73 and β=0.64, the technical solution of the present invention α and β can be selected from any value between 0 and 1, and the same effect can be achieved.

Claims (4)

1. a kind of asymmetrical watermark method based on Logistic chaotic map and Walsh sequence, is characterized in that, comprises the steps: Step 1: Construction of the feature matrix S Take an m×m image A _m×m as a carrier image, perform DCT transformation on the carrier image, select 4k×4k intermediate frequency coefficients from the DCT coefficients, and form a matrix B _4k×4k , Divide the matrix B _4k×4k into N blocks of non-overlapping 4×4 coefficient blocks, N=k×k, Denote the coefficient block of the i-th block as B _i , i∈[1,N], according to [u _i , s _i , v _i ]=svd(B _i ), perform singular value decomposition on the coefficient block of each block And extract the maximum singular value of each block, obtain N maximum singular values altogether, form characteristic matrix S with N described maximum singular values; Step 2: Construction of public key watermark W _p and private key watermark W _s Select a Walsh sequence of length N that is not related to the feature matrix S as the public key watermark W _p , namely According to the Logistic mapping dynamic equation x _n+1 = μ ₀ x _n (1-x _n ), the chaotic sequence X={x ₁ ,x ₂ ,Λ,x _n } is obtained, where μ ₀ is the branch parameter, μ ₀ ∈ (0,4), the initial value of x x ₀ ∈ (0,1), According to x _i =mod(round(x _i ×10 ⁸ ),2), The chaotic sequence X is converted into a sequence with a value of ±1, mod represents a modulo operation, and round represents rounding to the nearest integer, From the sequence with a value of ±1, intercept a sequence Y={y ₁ ,y ₂ ,Λ,y _N } with a length of N that is not related to the feature matrix S as the private key watermark W _s , namely The construction of the above public key watermark W _p and private key watermark W _s has no sequence; Step 3: Generate watermark image A' _m×m Calculate the weighted sum of the public key watermark W _p and the private key watermark W _s , and obtain the embedded watermark W _w according to the weighted sum construction. The construction method of the embedded watermark W _w is: W _w =αW _s +βW _p , α, β are preset parameters, α, β∈(0, 1), According to S'=S+λW _w , where λ is a preset parameter, the information of the embedded watermark W _w is embedded in the feature matrix S by addition to obtain the feature matrix S', and for each block in the feature matrix S' The singular value corresponding to the coefficient block is subjected to singular value inverse transformation to obtain a modified DCT coefficient, and the modified DCT coefficient is used to perform DCT inverse transformation on the carrier image to obtain an m×m watermark image A′ _m×m ; Step 4: Watermark detection Using the operation of the first step for the watermark image A' _m×m , the characteristic matrix S" is obtained, and the characteristic matrix S"=S+λW _W +n ₀ =S+λ(αW _s +βW _p )+ n ₀ , n ₀ represents the interference signal caused by various attacks, Use W _p _threshold and W _s _threshold to represent the public key detection threshold and private key detection threshold respectively, The setting method of the public key detection threshold _{Wp_threshold} is: in, is the mean value of the feature matrix S, is the mean value of the public key watermark W _p , is the energy of the public key watermark W _p , According to the setting method of the above public key detection threshold W _p _threshold, set the private key detection threshold W _s _threshold, Use W _p _test and W _s _test to represent the detection value of the public key detection and the detection value of the private key detection respectively, according to the formula: <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>W</mi> <mi>p</mi> </msub> <mo>_</mo> <mi>t</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <msup> <msub> <mi>W</mi> <mi>p</mi> </msub> <mi>T</mi> </msup> <mo>*</mo> <msup> <mi>S</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <msup> <msub> <mi>W</mi> <mi>p</mi> </msub> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>S</mi> <mo>+</mo> <mi>&amp;lambda;</mi> <mo>(</mo> <msub> <mi>&amp;alpha;W</mi> <mi>s</mi> </msub> <mo>+</mo> <msub> <mi>&amp;beta;W</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>n</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <msup> <msub> <mi>W</mi> <mi>p</mi> </msub> <mi>T</mi> </msup> <mo>*</mo> <mi>S</mi> <mo>+</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <msup> <msub> <mi>W</mi> <mi>p</mi> </msub> <mi>T</mi> </msup> <mo>*</mo> <msub> <mi>n</mi> <mn>0</mn> </msub> <mo>+</mo> <mfrac> <mrow> <mi>&amp;lambda;</mi> <mi>&amp;alpha;</mi> </mrow> <mi>N</mi> </mfrac> <msup> <msub> <mi>W</mi> <mi>p</mi> </msub> <mi>T</mi> </msup> <mo>*</mo> <msub> <mi>W</mi> <mi>s</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mfrac> <mrow> <mi>&amp;lambda;</mi> <mi>&amp;beta;</mi> </mrow> <mi>N</mi> </mfrac> <msup> <msub> <mi>W</mi> <mi>p</mi> </msub> <mi>T</mi> </msup> <mo>*</mo> <msub> <mi>W</mi> <mi>p</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> The W _p _test is calculated, and the W _s _test is calculated with reference to the same calculation method, Comparing the W _{p _test with the W p _threshold} , when W _p _test ≥ W _p _threshold, it is determined that the public key watermark W _p exists, otherwise, it is determined that the public key watermark W _p does not exist, Comparing the W _{s _test with the W s _threshold} , when W _s _test≥W _s _threshold, it is determined that the private key watermark W _s exists, otherwise, it is determined that the private key watermark W _s does not exist. 2. the asymmetric watermark method based on Logistic chaotic map and Walsh sequence according to claim 1, is characterized in that: In the first step, zigzag scanning is performed on the DCT coefficients, and the DCT coefficients are sorted from low to high in frequency. 3. the asymmetric watermark method based on Logistic chaotic map and Walsh sequence according to claim 1, is characterized in that: The image A _m×m is a grayscale image. 4. the asymmetric watermark method based on Logistic chaotic map and Walsh sequence according to claim 1, is characterized in that: The value range of the branch parameter μ ₀ in the second step is 3.5699456≤μ ₀ <4.